S3 is a permutation group on say 3 symbols 1,2,3. Then (123) represents a cyclic permutation of 3 length and so is of order 3.....In Z2, 1 bar denotes the residue class of 1, that ...
1) Order of S3 is 6 and that of Z2 is 2, therefore S3 X Z2 is of order 12...... 2) S3 is non abelian implies S3 X Z2 is non abelian....3) Any non abelian group of order 12 is eith...
When we divide any integer by 2, it leaves either 0 or 1 as the remainder....set of all the Integers which leaves zero as the remainder is denoted by 0 bar and set of those integer...